Gresham/Barlow School District
Mathematics Curriculum Map {Grade: 3rd }
2005/2006
|
Common Goals |
STANDARDS /FOUNDATIONS/
OSAT ELIGIBLE CONTENT AND CLASSROOM ONLY CONTENT (Words in bold text are for Classroom Instruction and
Assessment only. Italicized words are Eligible Content for items on the
OSAT.) |
*TIME
FRAME
|
*UNIT
|
*TOPICS |
*ASSESSMENT
|
**Vocabulary
|
Mathematical Problem Solving
(current language but under
revision) Select, apply, and
translate among mathematical representations to solve problems.
Apply and adapt a variety of
appropriate strategies to solve problems. Monitor and reflect on the
process of mathematical problem solving. Communicate mathematical
thinking coherently and clearly; use the language of mathematics to express
mathematical ideas precisely. Accurately solve problems
that arise in mathematics and other contexts. |
CONCEPTUAL UNDERSTANDING Interpret the concepts of
a problem-solving task and translate them into mathematics. PROCESSES AND STRATEGIES Choose strategies that
can work and then carry out the strategies chosen. VERIFICATION Produce identifiable
evidence of a second look at the concepts/strategies/calculations
to defend a solution. COMMUNICATION Use pictures, symbols,
and/or vocabulary to convey the path to the identified solution. ACCURACY Accurately solve
problems using mathematics. |
September-June |
Problem Solving
|
Problem
Solving Strategy Focus:
Make an
organized list and make a chart or a table
Classroom
Resources: (I.)[1]
10 Minute Math Activities and throughout the tasks (S.F.)[2]
Problem Solving Transparencies |
Sample open-ended prompts
available online at www.octm.org to be used
as work samples and scored with state scoring guide |
|
|
|
All Standards |
September-June |
Skill Practice and Review
|
Math
Journals:
2-3
times per week. The problems are set up so that they cycle through all
mathematics strands continuously through the year.
Classroom
Resources: (S.F.)
Spiral Review |
(S.F.) Assessment
Sourcebook: Diagnosing Readiness for Grade 3 pg. 43-46 |
|
|
Understand numbers, ways of
representing numbers, relationships among numbers, and number systems. Compute fluently and make
reasonable estimates. |
Read, write, order,
model, and compare up to 6 digit whole numbers. Identify the place value
and actual value of digits up to 6 digit whole numbers. Compose and decompose
whole numbers less than one thousand by place value. Add and subtract pairs of
up to four digit numbers. Mentally add or subtract
multiples of 10, 100, or 1000 to or from a number. Identify the operation
(add, subtract, multiply, or divide) for solving a problem. Develop and use
strategies (overestimate, underestimate, range of estimates) to make
reasonable estimates. Recognize which place
value will be the most helpful in estimating an answer. Make change for amounts
up to $10.00. Order and compare dollars
and coins by making equivalent amounts up to $10.00. |
Sept/Oct (6 weeks) |
Place Value and Addition & Subtraction
Review
|
Place value of ones, tens
hundreds, thousands Place value concepts
involved in additon and subtraction (with regrouping) Addition and subtraction
basic facts Relationshis among numbers
and fact families. (3+2=5, 2+3=5, 5-3=2, 5-2=3) Addition of 3-digit plus
3-digit whole numbers with regrouping Subtraction of 3-digit
minus 3-digit whole numbers with regrouping Rounding one-, two-, or three-
digit numbers to the nearst 10, 100, or 1000 for addition & subtraction
problems Concept of odd and even
numbers Place values to hundredths
place in the context of money Recognition and comparisons
for mixed amounts of pennies, nickels, dime quarters, half-dollar and dollar
coins up to $10.00 Money word problems with
and without regrouping up to $10.00 Location
of numbers and addition & subtraction on a numberline +/-
Inverse Operations (positive & negative numbers) September Calendar:
[3]
?
Counting by 2?s pattern
?
# of Days in School
using Base Ten pieces
?
Class Bank: +25 cents
for each day of school
?
Word for the Day ~ Area
and Perimeter Comparisons (words are selected from the grade level vocabulary
bank)
Students
particpate in games and activities that focus on building and recording
numbers up through 1,000, addition and subtraction with regrouping, and
addition and subtraction of money amounts up through $10. Classroom Resources: (I.) Combining and Comparing Book, Up and Down the Numberline, Landmark in the Hundreds Inv. 2 & 3, Mathematical Thinking at Grade 3 Inv. 2 (S.F.) Ch. 1, Ch. 2 Ch. 3 and Ch. 10 Place Value and Addition and Subtraction Literature Connections |
(I.) Assmt. Masters: 1, 2,
5, 28-31, 33-36 |
Ordinal number Digit Decimal point Decimal number Expanded form Commutative property Associative property Equation Expression Inequalities |
|
Understand patterns,
relations, and functions. Represent
and analyze mathematical
situations and
structures using algebraic symbols. Analyze
characteristics and properties of
two- and
three-dimensional geometric
shapes and develop mathematical
arguments
about geometric relationships. Use
visualization, spatial reasoning,
and geometric modeling
to solve problems. Specify
locations and describe spatial
relationships using coordinate
geometry and other representational
systems Apply
transformations and use symmetry
to analyze mathematical
situations. |
Describe, extend, and make generalizations about numeric
and geometric
patterns (e.g., increasing the number of sides of two-dimensional geometric figures in
sequence; consecutive odd
numbers). Supply
a missing element in or determine a rule that extends number patterns
involving addition and multiplication by a single-digit number. Generate
a pattern or sequence from a verbal, written, and pictorial description. Use
letters, boxes, or other symbols to stand for a missing number in simple
expressions or equations. Identify,
describe, compare, and classify common three-dimensional geometric
objects: cubes, prisms, spheres, pyramids, cones, and cylinders. Compare
and classify solid geometric shapes (e.g., triangular, pyramid,
cube, rectangular prism) according to the number and shapes
of faces, edges, and vertices. Recognize
and identify attributes of three-dimensional geometric shapes
(faces, edges, vertices), including attributes of shapes in the environment. Model
three-dimensional shapes including cubes, rectangular prisms,
spheres, pyramids, cones, and cylinders. Put
shapes together and take them apart to form other shapes. Recognize
three-dimensional geometric shapes (e.g., cube, cone, cylinder,
pyramid, and sphere) in the environment and from different
perspectives. Describe
paths for moving from one location to another on a grid. Identify
line and rotational symmetry Predict
and describe the results of performing reflections, rotations and
translations of triangles. |
Oct/Nov (6 Weeks) |
Geometry and Patterning |
Perimeter of geometric
shapes such as triangles, quadrilaterals (trapezoid, paralellogram,
rectangle, rhombus, square), pentagons, hexagons, octagons, in meters and
centimeters Missing elements in a
geometric pattern Attributes of geometric
figures Properties of geometric
figures (Congruence and Similarity) Reflections and rotations of line segments, angles,
triangles, quadrilaterals, circles (including location of diameter &
radius), Explore turns and pathways Recognition and
description of line segments, angles (acute, right, obtuse), spheres, cubes,
prisms, and pyramids Angle Identification
(acute, obtuse, 90?) Closed and not-closed
figures 3-dimensional shapes shown
"unfolded" in 2-dimensional representations Line and rotational
symmertry October Calendar: ?
Counting by 3?s Pattern ?
# of Days in School
using Base Ten pieces ?
Class Bank: +25 cents for
each day of school ?
Word for the Day: Area
and Perimeter Comparisons
(words are selected from
the grade level vocabulary bank), ?
About Time: What time
will it be 3 minutes from ?
now? 3 minutes ago? November Calendar: ?
Counting by 4?s Pattern ?
# of Days in School
using Base Ten pieces ?
Class Bank: +25 cents
for each day of school ?
Word for the Day: Area
and Perimeter Comparisons (words are selected from the grade level vocabulary
bank) ?
About Time: Daily
Schedule (duration of
time in minutes and hours) Students participate in
games and activities that focus on geometric patterning, perimeters,
coordinates, and translations and symmetry Classroom Resources: (I.) Flips, Turns, and Area,
Exploring Solids and Boxes, Turtle Paths (S.F.) Ch. 8, and 4-9 pg.
218 |
(I.) Assmt. Masters: 2,
13-16, 38-40, 47-50 |
Growing pattern Expression Plane Vertex Parallel lines Acute angle Right angle (90?) Flip Congurence Slide Symmetry Ordered pair |
|
Compute fluently and make
reasonable estimates. Understand meanings of
operations and how they relate to one another. Apply transformations and
use symmetry to analyze mathematical situations. |
Develop and evaluate
strategies for multiplying whole numbers. Develop and acquire
efficient strategies for determining multiplication and division facts 0-9. Find areas of rectangular
arrays. Represent situations
using models of multiplication and division (e.g., repeat addition, equal
groups of objects, arrays, repeated subtraction, equal grouping, sharing
equally) Use the commutative and
associative properties of multiplication to simplify calculations Describe the effects of
multiplying or dividing by a whole number. Demonstrate the zero
property for multiplication and identity property for multiplication and
division. Multiply a two-digit
number by a one-digit number. Demonstrate the counting
skills of skip counting as they relate to multiplication facts. |
Dec/Jan (7 Weeks) |
Multiplication and Division |
Skip counting and the
concept of multiples Area of arrays Multiplication basic facts Division basic facts Reproduction of a pattern
in multiples of the numbers 2 through 9, monetary relationships under $10.00,
relationships between numerator and denominator of a fraction using common
multiples, divisions or arrangements of two dimensional geometric figure Relationship between two
quantities such as number of people who can be seated at a table & the
number of tables needed Mathematical relationships
and patterns in table format Factors in equations ( __
x 5 = 15) Multiplication patterns on
the 100s Chart and with a calculator constant Multiplication and division
basic facts strategies December Calendar: ?
Counting by 5?s Pattern ?
# of Days in School
using Base Ten pieces ?
Class Bank: +25 cents
for each day of school ?
Word for the Day: Area
and Perimeter Comparisons (words are selected from the grade level vocabulary
bank) ?
About Time: What time
was it 6 hours ago? What time will it be in 6 hours? January Calendar: ?
Counting by 6?s Pattern ?
# of Days in School
using Base Ten pieces ?
Class Bank: +25 cents
for each day of school ?
Word for the Day: Area
and Perimeter Comparisons (words are selected from the grade level vocabulary
bank) ?
Measurement Records:
Temperature Highs and Lows Chart and Line Graphs ?
About Time: time
comparison between time here and Portland, Maine Students particpate in games
and activities that focus on multiples on the calculator, multiplication and
division basic facts through nine Classroom Resources: (I.) Things that Come in Groups and Mathematical Thinking at Grade 3 Inv. 2 (S.F.) Ch. 5, 6, and 7 |
(I.) Assmt. Masters: 7-11 |
Multiple Identity Array Factors Square number Remainder |
|
Compute fluently and make
reasonable estimates. Represent and analyze
mathematical situations and structures using algebraic symbols. |
Multiply a two-digit
number by a one-digit number. Identify
the operation (add, subtract, multiply, or divide) for solving a
problem. Develop and use
strategies (overestimate, underestimate, range of estimates) to make
reasonable estimates. Recognize which place
value will be the most helpful in estimating an answer. Identify and apply a
relationship between two quantities (e.g., If four people can be seated at
one table, how many tables are needed to seat 24 people?). |
Feb (4 Weeks) |
Larger number
multiplication, Mixed Practice Review and Estimation |
Multiplication facts
through twelves 2 digit multiplcation Mixed Practice and 2-Step
Story Problems using Student and Teacher Generated Word Problems (All
Operations) Estimation Strategies February Calendar: ?
Counting by 7?s Pattern ?
# of Days in School
using Base Ten pieces ?
Class Bank: +25 cents
for each day of school ?
Word for the Day: Area
and Perimeter Comparisons (words are selected from the grade level vocabulary
bank) ?
Measurement Records:
(foot, yards, counting by 12) ?
About Time: Sunrise and
Sunset Times (duration of time in minutes and hours of daylight) Students particpate in games
and activities that focus on creating and solving story problems, rounding
and estimations skills, and mixed operations practice games Classroom Resources: (I) Landmarks in the Hundreds and Things that Come in Groups (S.F.) Ch. 11 plus story
problem examples can be found throughout Ch 2, 3, 5, 6, 7 that can be
modified to fit teacher purposes |
(I.) Assmt. Masters:
21,23-26 |
|
|
Select and use appropriate
statistical methods to analyze data. Formulate questions that can
be addressed with data and collect, organize, and display relevant data to
answer them. Develop and evaluate
inferences and predictions that are based on data. |
Determine the mode and
range of a set of data. Ask and answer
simple questions that can be answered by collecting, organizing, and
displaying data. Represent and interpret data using tally charts,
pictographs, and bar graphs, including identifying the mode and range. Draw conclusions and make
predictions and inferences from tally charts, pictographs, or bar graphs. |
March/April (4 Weeks) |
Statistics |
Data analysis from charts
or tables with five or fewer entries, horizontal & vertical bar graphs
with five or few bars, & pictographs with 10 or fewer data pieces (data
limited to whole numbers up to 200, whole dollar amounts up to $100) Graph creation using
pencil/paper and computer software Mode Range Possible Outcomes March Calendar: ?
Counting by 8?s
Pattern, ?
# of Days in School
using Base Ten pieces, ?
Class Bank: +25? for
each day of school, ?
Word for the Day: Area
and Perimeter Comparisons (words are selected from the grade level vocabulary
bank) ?
Measurement Records:
(pounds, ounces, grams) ?
About Time: What was
the time 19 hours ago? What were you doing then? ?
Measurement tool
riddles ( e.g. I measure length. I have 100 units. What am I? A. A meter stick.) Students particpate in games
and activities that practice probability concepts and data collection using
charts and graphs Classroom Resources: http://www.pps.k12.or.us/instruction-c/math/01_02_lesson_plans/3probability.pdf (S.F.) Ch. 4 Sections B
& C Ch. 12 Section B Statistics and Probability Literature Connections |
|
Survey Line plot Mode Pictograph Range Line graph Coordinate graph Probability (chance) |
|
Understand numbers, ways of
representing numbers, relationships among numbers, and number systems. Understand measurable
attributes of objects and the units, systems, and processes of measurement. Apply appropriate techniques,
tools, and formulas to determine measurements. |
Order, model, compare,
and identify commonly used fractions (halves, thirds, fourths, eighths,
tenths) using concrete models and visual representations. Develop understanding of
fractions as parts of unit wholes, as parts of a collection, as locations on
number lines, and as divisions of whole numbers. Locate whole numbers and
common fractions on a number line. Select the most
appropriate tool and metric unit to measure length, time, weight, and volume. Compare units of measure
between customary and metric systems (e.g., inches > centimeters, liters
< gallons). Understand and explain
the need for using standard units. Determine elapsed time
for given activities using representations of analog and digital clocks. Tell time to the nearest
minute using an analog clock. Describe temperature
changes and concepts as they occur in daily situations. Determine measurements of
length to the nearest centimeter and nearest meter. Estimate the length of
objects in meters and centimeters. Determine measurements of
volume to the nearest milliliter or liter of measuring cups, beakers, or
graduated cylinders. Estimate volume of
objects in milliliters and liters. Determine measurements of
weight to the nearest gram and kilograms. Estimate weight of
objects in grams and kilograms. Find areas of rectangular
arrays. |
Apr/Jne (8 Weeks) |
Fractions & Measurement |
Linear measures using metric
units Weight measures using metric
units Volume/capacity measures
using metric units Comparison between customary
and metric units using real world referents Time Temperature April Calendar: ?
Counting by 9?s Pattern ?
# of Days in School
using Base Ten pieces ?
Class Bank: +25? for
each day of school ?
Word for the Day: Area
and Perimeter Comparisons (words are selected from the grade level vocabulary
bank) ?
Fraction a Day Pattern
Block Numberline (fraction notation, equivalence, mixed and improper fraction
notation) ?
Geometry Riddles: What
am I? (e.g. I have a right
angle, I have 3 sides. What am I? A. An equilateral triangle?) May/June Calendar: ?
Counting by 10?s
Pattern ?
# of Days in School
using Base Ten pieces ?
Class Bank: +25 cents
for each day of school, ?
Word for the Day: Area
and Perimeter Comparisons (words are selected from the grade level vocabulary
bank) ?
Fraction a Day: Pattern
Block Numberline (fraction notation, equivalence, mixed and improper fraction
notation) ?
Money Riddles: (e.g. I
have __ coins. I have ___ cents. What coins do I have? ) Students particpate in games
and activities that reinforce fraction concepts and measurement skills Classroom Resources: (I.) From Paces to Feet,
Fair Shares Portland Public Supplemental
Packet at: http://www.pps.k12.or.us/instruction-c/math/01_02_lesson_plans/3measurement.pdf (S.F.) Ch. 9, Ch. 10 Ch. 12
Section A Fraction and Measurement Literature Connections |
(I.) Assmt. Masters: 18-20,
42-96 |
|